On hyperideals in left almost semihypergroups.
Summary: This paper deals with a class of algebraic hyperstructures called left almost semihypergroups (LA-semihypergroups), which are a generalization of LA-semigroups and semihypergroups. We introduce the notion of LA-semihypergroup, the related notions of hyperideal, bi-hyperideal, and some properties of them are investigated. It is a useful nonassociative algebraic hyperstructure, midway between a hypergroupoid and a commutative hypersemigroup, with wide applications in the theory of flocks, and so forth. We define the topological space and study the topological structure of LA-semihypergroups using hyperideal theory. The topological spaces formation guarantee for the preservation of finite intersection and arbitrary union between the set of hyperideals and the open subsets of resultant topologies.
scientific article; zbMATH DE number 5964875
scientific article